The answer for a measure of ∠P = 72.92° using congruence of the triangle.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
As given ∠P = ∠Q and ∠R=34.15
We know that sum of all angles in a triangle = 180 °
So 2∠P + ∠Q = 180
2∠P = 180-34.15 = 145.85
∠P = 72.92
So the measure of ∠P is 72.92°
Learn more about congruent, by the following link.
https://brainly.com/question/1675117
#SPJ1
Jacob has a coin collection. He keeps 5 of the coins in his box, which is 10% of the collection. How many total coins are in his collection?
The number of coins that are in Jacob's collection is 50
How to find the number of coinsinformation from the problem
Jacob has a coin collection
He keeps 5 of the coins in his box, which is 10% of the collection
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
10%
= 10 percent
= 10 / 100
= 0.1
The factor 0.1 of the total number of coin is 5
let the total number be x
0.1 * x = 5
0.1x = 5
x = 5 / 0.1
x = 50
The total number of coins is 50
Learn more about percent here:
https://brainly.com/question/29230566
#SPJ1
How many three-letter sequences can be made from the word "COMBINATORICS" where no 2 letters can be the same?
The number of three-letter sequences that can be made from the word "COMBINATORICS" where no 2 letters can be the same is 720 ways
How to find the number of waysThe question is asking of permutation
arranging the letters without repeating a word gives
COMBINATORICS ⇒ COMBINATRS
The newly arranged word gives 10 letters and arranging 10 letters by taking 3 at a time is 10P₃
The required permutation is 10P₃
10P₃
= 10! / (10 - 3)!
= 10! / 7!
= 720
= 720 ways
Learn more about permutation here:
https://brainly.com/question/28065038
#SPJ1
M. |h-8| = |h+ 10|
Find the value of the variable which satisfies the equation.
True or false
A credit union is an example of a service cooperative.
Answer:
false
Step-by-step explanation:
Credit Unions are not-for-profit financial service cooperatives
help please. what are these? thank you.
8. The value of x is 9
9. The value of x is 9
10. The value of x is 36
11. The value of x is 8
Calculating the value of xFrom the question, we are to determine the value of x in the given diagram.
8.
2x + 12 = 5x - 15
Collect like terms
12 + 15 = 5x - 2x
27 = 3x
3x = 27
Divide both sides by 3
3x/x = 27/3
x = 9
9.
8x - 63 = 4x - 27
Collect like terms
8x - 4x = -27 + 63
4x = 36
Divide both sides by 4
4x/4 = 36/4
x = 9
10.
(3x - 18)° = 90°
3x - 18 = 90
Add 18 to both sides
3x - 18 + 18 = 90 + 18
3x = 108
Divide both sides by 3
3x/3 = 108/3
x = 36
11.
Since the angles are complementary, we can write that
(3x)° + (8x + 2)° = 90°
3x + 8x + 2 = 90
11x + 2 = 90
Subtract 2 from both sides of the equation
11x + 2 - 2 = 90 -2
11x = 88
Divide both sides by 11
11x/11 = 88/11
x = 8
Hence, the value of x is 8
Learn more on Calculating the value of x here: https://brainly.com/question/19703680
#SPJ1
HELP Which expression is equivalent to the given expression?
5x−2
A: 2−5x
B: 2x−2+3x
C: 3−5+2x
D: 5x−2x
The equation of the line that passes through the given points (4,6) and (4.2)
Answer: ___________________________________________________
x = 4
2/3n + 4 = -26 we cant figure this out pls help
Answer:
n = -45
Step-by-step explanation:
2/3n + 4 = -26
subtract 4 from both sides:
2/3n + 4 - 4 = -26 - 4
2/3n = -30
divide both sides by 2/3:
(2/3n)/(2/3) = (-30)/(2/3)
n = -45
Answer:
n=-45
Step-by-step explanation:
2/3n+4=-26
-4. -4
2/3n=-30
/2/3. /2/3
n=-30/1 *3/2
n=-90/2
n=-45
Hopes this helps please mark brainliest
Using your same definition, what are the zeros of this function?
The zeros of the given function are -2, and 1 in the represented graph.
What are the zeros in the function?A function's zeros are the values of x when f(x) equals 0. As a result, its name. This indicates that when f(x) = 0, x is a function zero. When the graph crosses through x = a and is considered to be the function's zero. As a result, (a, 0) is a function zero.
The graph is given in the question,
According to the shown graph, the function in the given graph has located at the x-axis of the plane, which is the location or coordinates from where the line crosses which are -2, and 1.
Therefore, the zeros of the given function are -2, and 1 in the represented graph.
To learn more about the zeros in the function click here:
https://brainly.com/question/16633170
#SPJ1
Combine the like terms to create an equivalent expression 5 + 2m + 3n + 6
Answer:
2m + 3n + 11
Step-by-step explanation:
You cannot combine the m and the n terms, but you can combine 5 and 6
The equation x² - 6x = 72 has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
The equation x² - 6x = 72 has a solution between 4 and 5
Use a trial and improvement method to find this solution.
There are a number of "improvement" techniques that can be used to improve an estimate of a solution to a polynomial. Some of them use the polynomial itself to form the iterator function.
Iterator
There are a number of ways we can solve the given equation for x. Often, at least one of these will converge when used for improving the estimated value of x.
x₁ = ([tex]x^{2}[/tex] -72)/6 . . . . . . . add 6x-72, divide by 6
x₂ = 72/(x^2 -6) . . . . . . . factor out x and divide by its coefficient
x₃ = ∛(72 +6x) . . . . . . . add 6x and take the cube root
The first two of these iterators tend to diverge. For x = 4.5, they give ...
x₁ = (4.5³ -72)/6 = 3.1875
x₂ = 72/(4.5² -6) = 5.0526
Both of these stray out of the given interval of [4, 5].
However, the third one tends to converge, so can give us a useful approximation in one iteration:
x₃ = ∛(72 +6×4.5) ≈ ∛99 ≈ 4.6261
Second iteration
Applying this again, we get ...
x ≈ ∛(72 +6·4.6261) ≈ 4.6378
The approximate root to 1 decimal place is 4.6.
Additional comment
One of the quickest converging iterators is that provided by Newton's method. For finding the solution to f(x) = 0, it uses ...
x₁ = x -f(x)/f'(x) . . . . . . . where f'(x) is the first derivative
For this problem, we can define ...
f(x) = [tex]x^{2}[/tex] -6x -72 ⇒ f'(x) = 3x^2 -6
x₁ = x -([tex]x^{2}[/tex] -6x -72)/(3x^2 -6) = (3[tex]x^{2}[/tex] -6x -[tex]x^{2}[/tex] +6x +72)/(3x^2 -6)
x₁ = (2[tex]x^{2}[/tex] +72)/(3x^2 -6)
Then for x = 4.5, the "improved" solution is ...
x₁ = (2(4.5³) +72)/(3(4.5²) -6)) = 254.25/54.75 = 339/73 ≈ 4.6438
A second iteration gives ...
x ≈ 4.639026 . . . . accurate to 5 decimal places
Hence with this iterator, the number of accurate decimal places tends to double with each iteration.
To learn more about Iteration click here https://brainly.com/question/25754804
#SPJ9
2500 dollars is placed in an account with an annual interest rate of 9%. To the nearest year, how long will it take for the account value to reach 7500 dollars?
It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
According to the question,
We have the following information:
2500 dollars is placed in an account with an annual interest rate of 9%.
We know that following formula is used to find simple interest:
Simple interest = principal*rate*time/100
Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:
7500-2500
5000
So, we have the following expression:
(2500*9*t)/100 = 5000
Now, using cross multiplication method:
t = (5000*100)/(2500*9)
t = 200/9 years
t = 22.2 years
Now, the nearest year will be 22 years.
Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
To know more about interest rate here
https://brainly.com/question/11566183
#SPJ1
Identify the number line that correctly displays the solution x ≥ 3.
The Graph of x ≥ 3 is attach below
The definition of a linear inequality
The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.
What does a linear inequality in mathematics look like?
What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being used in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).
Learn more about linear inequality
brainly.com/question/371134
#SPJ1
Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The parabola equation in its vertex form is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?From the question, we have the function to be
f(x) = 3x²
Also, we have the vertex to be given as
Vertex = (5, 9)
A quadratic function takes the form:
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
So, we can rewrite f(x) = 3x² as follows
f(x) = 3(x - 0)² + 0
By comparing the equations, we have
a = 3
Also, by comparison, we have
(h, k) = (5, 9)
Substitute a = 3 and (h, k) = (5, 9) in f(x) = a(x - h)² + k
So, we have
f(x) = 3(x - 5)² + 9
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
Read more about parabola at
brainly.com/question/1480401
#SPJ1
A boat sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 feet find the length of two sides of the sail.
Base of the Sail is 12 feet and Height of the Sail is 5 feet
What is Right Angle Triangle?
A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Solution:
Accroding to the Question,
Let, Base = x and Height = y
x = 7 + y
Using the Pythagorous Theorem
[tex]Base^{2} + Perpendicular^{2} = Hypotenuse^{2}[/tex]
[tex]x^{2} + y^{2} = 13^{2}[/tex]
Using the above mentioned relation
49 + y^2 + 14y + y^2 = 169
2y^2 + 14y - 120 = 0
Discriminant = 34
y = 5, -12
The length of a sail can not be neegative, therefore y = 5
From the equation 1, x = 12
To learn more about Right Angle Triangle from the given link
https://brainly.com/question/64787
#SPJ1
Juan works 40 hours per week. He earns $9 per hours. How much does Juan earn in one week?
Answer:
2,500
Step-by-step explanation:
40 × 7 × 9
=2,500d dollars
Need help asap!!!!!!
Answer:
Step-by-step explanation:
The original rectangle has dimensions of 70 x 35.
Therefore, we can find its perimeter and area with the standard formulas.
A = 70 * 35
= 2450 square units
P = 2(70) + 2(35)
= 210 units
The new rectangle is dilated by a 1/5 factor, so both dimensions will be one fifth the size of the original. When you have a scale factor that is 1 over some number, you can find the new measurement by dividing by that denominator.
Therefore, new rectangle's dimensions are:
70 ÷ 5 = 14
35 ÷ 5 = 7
Now, find area and perimeter of the new rectangle.
A = 14 * 7
= 98 square units
P = 2(14) + 2(7)
= 42 units
Which expression is equivalent to N/4+n/4+n/4+n/4
Answer: 4[tex]\frac{n}{4}[/tex]
Step-by-step explanation:
PLEASE HELP ME
Simplify 6/7c − 5/9d − 1/2 c + 1/3d
A: 514c − 29d
B: 59c + 412d = 59c +13d
C: 59c − 412d = 59c −13d
D: 514c + 29d
The simplified form of the expression [tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex] is [tex]\frac{5}{14}c-\frac{2}{9}d[/tex]
How to simplify an expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Therefore, let's simplify the expression as follows:
To simplify an expression means to write an equivalent expression which contains no similar terms.
his means that we will rewrite the expression with the fewest terms possible.
Hence,
[tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex]
combine like terms
[tex]\frac{6}{7}c-\frac{1}{2}c-\frac{5}{9}d+\frac{1}{3}d[/tex]
Do the arithmetic
[tex]\frac{12c-7c}{14}+\frac{-5d+3d}{9}[/tex]
[tex]\frac{5}{14}c-\frac{2}{9}d[/tex]
learn more on expression here: https://brainly.com/question/26857779
#SPJ1
How do I solve this?
-27 v-54 v²-36 v³
The equation -27v - 54v²-36v³ cannot be solved as it doesn't have a factor
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
There are 3 main types of equation
1. Slope-intercept : y = mx + c
where m is the slope and b is the y-intercept
2. Point-slope : [tex](y - y_{1} ) = m (x - x_{1} )[/tex]
Where m is the slope and [tex](x_{1},y_{1})[/tex] is a point on the line
3. Standard : Ax + By = C
where A, Band C are constants
Factorizing the equation we get
-3v(9 + 18v + 12v²)
= -9v(4v² +6v +3)
(4v² +6v +3) as this equation doesn't have a factor it is difficult to solve
To learn more about an equation from the given link
https://brainly.com/question/18831322
#SPJ1
Answer the questions below! Thank you^^
a) The Factor of -4x² + 12x is 4x( -x +3)
b) The multiplication of (4.8x)(4x) is 19.2x²
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
-4x² + 12x
Now, factorizing
4x²= 2 x 2× x × x
12x = 2 ×2× 3 × x
So, the factor can be
-4x² + 12x
= -2 x 2× x × x + 2 ×2× 3 × x
= 4x( -x +3)
and, (4.8x) ×4x
= 4.8 × 4 × x × x
= 19.2x²
Learn more about algebra here:
https://brainly.com/question/24875240
#SPJ1
Use the diagram to answer both questions.
The value of x : 56
What is Angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Given,
∠A = (2x - 6)°
∠B = 74°
Since, we have to find the value of x
we have to find it by Linear equation
∠A + ∠B = 180°
Substituting the values we have
(2x - 6)° + 74° = 180°
2x - 6 + 74 = 180
2x + 68 = 180
2x = 180 - 68
2x = 112
x = 112/2
x = 56
The value of ∠A = 56 - 6 = 60°
Hence, The value of x = 56
To learn more about Angles click on the link
https://brainly.com/question/25716982
#SPJ1
Factor the polynomial completely.
x4 + 2x2 - 35
Answer:
[tex](x^2+7)(x^2-5)[/tex]
A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 16 years, assuming the account earns a 6% return.
The person has to deposit $1948.05 per year.
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
In the given question, to find the value to be added per year we will use the formula.
[tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t} - 1}[/tex]
Here A = 50,000
r (rate of interest) = 6 % or 0.06.
n = 1
t = 16
P = value deposit per year
On substituting the values,
[tex]P= \frac{50000 \times 0.06} {(1 +0.06)^{16} - 1}[/tex]
P = 3000 / 2.54- 1
= $1948.05 .
Therefore, person has to deposit $1948.05 per year.
To learn more about compound interest from the link
https://brainly.com/question/24274034
#SPJ1
Factorise 32s+40.
Write your answer as a product with a whole number greater than 1.
The expression when factored out is 8(4s + 5)
How to determine the factored expression?From the question, we have the following expression that can be used in our computation:
32s + 40
The terms of the above expression are:
32s and 40
And the factor of 32 and 40 is
Factor = 8
So, we divide 32s and 40 by 8
The results of these divisions are
32s/8 = 4s
40/8 = 5
So, we have the following results
32s + 40 = 8(4s + 5)
Hence, the factored expression is 8(4s + 5)
Read more about expressions at
brainly.com/question/18631189
#SPJ1
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Question 7(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Three different recipes each make a different number of cookies and require a different amount of flour.
Recipe 1: 3 dozen cookies; 4.5 cups of flour
Recipe 2: 4 dozen cookies; 6 cups of flour
Recipe 3: 5 dozen cookies; 7.5 cups of flour
Determine if the three recipes use a proportional amount of flour.
Yes, it is proportional because the cookies increase by 1.5 dozen for every 1 cup of flour.
Yes, it is proportional because the ratios between the number of cookies and cups of flour are all equivalent.
No, it is not proportional because the number of cookies and cups of flour could not be zero at the same time.
No, it is not proportional because the ratios between the number of cookies and cups of flour are not all equivalent.
Answer:
Yes, All the three recipes use a proportional amount of flour.
Step-by-step explanation:
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
There are three different recipes to make cookies for different amount of flour.
Recipe 1 = 3 dozen cookies and 4.5 cups of flour
Recipe 2 = 4 dozen cookies and 6 cups of flour
Recipe 3 = 5 dozen cookies and 7.5 cups of flour
Now,
To check that all the recipes in proportion, we check the amount of flour for 1 dozen cookies.
For recipes 1;
The amount of flour = 4.5 / 3
= 1.5
For recipe 2;
The amount of flour = 6 / 4
= 1.5
For recipe 3;
The amount of flour = 7.5 / 5
= 1.5
Clearly, All are the same amount to make 1 dozen of cookies.
So, The all recipes are in proportions.
Therefore, All the three recipes use a proportional amount of flour.
Multi-Step Problem You are choosing between two electricity providers. The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. a. Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service. Write the two equations representing the cost of each company's service for one month.
The total cost for Zap Electric Company and Bolt Electric Company are y = 0.06r + 6.55 and y = 0.12r + 2.83
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.
The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:
y = 0.06r + 6.55
The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:
y = 0.12r + 2.83
The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Write these fractions as percentage 2/3
Answer: 66%
Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, [tex]\frac{1}{4}[/tex] is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.
hope this helps!
please give brainliest!
order from greasest to least ; 3.84,3.789,3,3 41/50
Answer: 3.84 , 3 41/50 , 3.789 , 3
